Topic
Fourier series
About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.
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TL;DR: Within the Lindblad formalism, the authors considered an interacting spin chain coupled locally to heat baths and investigated the dependence of the energy transport on the type of interaction in the system as well as on the overall interaction strength.
Abstract: Within the Lindblad formalism we consider an interacting spin chain coupled locally to heat baths. We investigate the dependence of the energy transport on the type of interaction in the system as well as on the overall interaction strength. For a large class of couplings we find a normal heat conduction and confirm Fourier's Law. In a fully quantum mechanical approach linear transport behavior appears to be generic even for small quantum systems.
72 citations
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TL;DR: In this paper, the Carleson-Hunt theorem was strengthened by showing that the partial sum operators for Fourier series and integrals can be approximated by a variation norm of the Menshov-Paley-Zygmund theorem.
Abstract: We strengthen the Carleson-Hunt theorem by proving $L^p$ estimates for the $r$-variation of the partial sum operators for Fourier series and integrals, for $p>\max\{r',2\}$. Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.
72 citations
TL;DR: In this paper, the authors established local and global existence results for Boussinesq type equations on a circle, employing Fourier series and a fixed point argument, using a fixed-point argument.
Abstract: We establish local and global existence results for Boussinesq type equations on a circle, employing Fourier series and a fixed point argument.
72 citations
TL;DR: In this article, a modified Fourier-Ritz approach was developed to study the free in-plane vibration for the orthotropic circular, annular and sector plates with general boundary conditions, and several auxiliary closed-form functions were added to the standard Fourier cosine series to obtain a robust function.
72 citations
TL;DR: In this paper, a semi-analytical method is described and applied to investigate the free vibration of the functionally graded (FG) sandwich doubly-curved panels and shells of revolution with arbitrary boundary conditions, in which the first-order shear deformation theory is considered.
72 citations